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Matematicheskoe modelirovanie, 2016, Volume 28, Number 5, Pages 3–23 (Mi mm3726)  

This article is cited in 6 scientific papers (total in 6 papers)

On construction of images of layered media in inverse scattering problems for the wave equation of acoustics

A. V. Baev

Lomonosov Moscow State University
References:
Abstract: Two-dimensional inverse scattering problems for the wave equation of acoustics on determining the density and acoustic impedance of the medium were studied. A necessary and sufficient condition for the unique solvability of these problems in the form of the energy conservation law is established. It is proved that this condition is that for each pulse oscillation source, located on the boundary of the half-plane, the flow of energy of the scattered waves is less than the energy flux of waves propagating from the boundary of the half-plane. This shows that the inverse scattering problems of dynamic acoustics and geophysics in the case of the law of conservation of energy is possible to determine the elastic-density parameters of the medium. The results allow to considerably extend the class of mathematical models currently used in the solution of multidimensional inverse scattering problems. Several special questions of interpretation for solutions of inverse problems are regarded.
Keywords: equations — acoustic, Klein–Gordon, Gel'fand–Levitan; Galerkin method, eikonal, density, acoustic impedance.
Received: 22.01.2015
English version:
Mathematical Models and Computer Simulations, 2016, Volume 8, Issue 6, Pages 689–702
DOI: https://doi.org/10.1134/S2070048216060041
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. V. Baev, “On construction of images of layered media in inverse scattering problems for the wave equation of acoustics”, Mat. Model., 28:5 (2016), 3–23; Math. Models Comput. Simul., 8:6 (2016), 689–702
Citation in format AMSBIB
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\by A.~V.~Baev
\paper On construction of images of layered media in inverse scattering problems for the wave equation of acoustics
\jour Mat. Model.
\yr 2016
\vol 28
\issue 5
\pages 3--23
\mathnet{http://mi.mathnet.ru/mm3726}
\elib{https://elibrary.ru/item.asp?id=26414256}
\transl
\jour Math. Models Comput. Simul.
\yr 2016
\vol 8
\issue 6
\pages 689--702
\crossref{https://doi.org/10.1134/S2070048216060041}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84994817756}
Linking options:
  • https://www.mathnet.ru/eng/mm3726
  • https://www.mathnet.ru/eng/mm/v28/i5/p3
  • This publication is cited in the following 6 articles:
    1. Sergey Kabanikhin, Maxim Shishlenin, Nikita Novikov, Nikita Prokhoshin, “Spectral, Scattering and Dynamics: Gelfand–Levitan–Marchenko–Krein Equations”, Mathematics, 11:21 (2023), 4458  crossref
    2. Sergey I. Kabanikhin, Nikita S. Novikov, Maxim A. Shishlenin, “Gelfand-Levitan-Krein method in one-dimensional elasticity inverse problem”, J. Phys.: Conf. Ser., 2092:1 (2021), 012022  crossref
    3. D. Klyuchinskiy, N. Novikov, M. Shishlenin, “A modification of gradient descent method for solving coefficient inverse problem for acoustics equations”, Computation, 8:3 (2020), 73  crossref  isi
    4. A. V. Baev, “On solution of an inverse non-stationary scattering problem in a two-dimentional homogeneous layered medium by means of τp Radon transform”, Math. Models Comput. Simul., 10:5 (2018), 659–669  mathnet  crossref  elib
    5. A. V. Baev, “Radon transform for solving an inverse scattering problem in a planar layered acoustic medium”, Comput. Math. Math. Phys., 58:4 (2018), 537–547  mathnet  crossref  crossref  isi  elib
    6. A. M. Denisov, “Iterative method for solving an inverse coefficient problem for a hyperbolic equation”, Differ. Equ., 53:7 (2017), 916–922  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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